Several approaches for measuring fluid shear viscosities using quartz crystals have evolved since Quimby originated the technique of measuring solids by attaching them to a quartz crystal. The Quimby composite resonator (QCR) functions like a quartz crystal microbalance (QCM) in the limit where the measurand becomes a thin film, and its elasticity is neglected. Mason first adapted the technique for measuring liquids, and this method is still widely used. Stockbridge has also used quartz crystal techniques to measure gases. In these applications, the crystal resonator is measured without, and then with, the loading of the measurand fluid. Ensuing changes can be recorded as changes in frequency, phase, or impedance level, from which the unknown measurand properties can then be inferred.
Prior art devices have provided numerous equivalent electrical circuits that model the piezoresonator, and describe the behavior of the piezoresonator when its surface is subjected to various loading conditions. The most popular equivalent electrical circuit is the Butterworth-Van Dyke (BVD) network, which consists of a capacitance C0, shunted by an R1, L1, and C1 series arm. The series arm is the manifestation of the piezoelectrically induced vibratory motion at a single isolated resonance. The BVD lumped circuit then evolved into the more elaborate broad-band, multi-mode, transmission-line networks that place the mechanical boundary loadings and piezoelectric excitation mechanism in series at the surfaces. Current dynamic techniques for measuring fluid shear viscosities using quartz, or other piezoelectrics, rely upon exposing the resonator surface to a measurand tank whose extent greatly exceeds the penetration depth (δ) of the evanescent shear mode excited by the active element. This configuration allows the effect of the loading parameters to be expressed concisely. Perturbation of the electrical equivalent circuit parameters of the resonator by the fluid loading permits calculation of the mass density—shear viscosity product, but does not allow calculation of these quantities separately.
FIGS. 1A and 1B are top and end views of a typical prior art measurand tank.
Referring now to FIG. 1A, the prior art measurand tank 1 contains a shear wave piezoelectric transducer 2 that is submerged in the measurand fluid 3. The piezoelectric transducer 2 produces acoustic motion in the fluid 3 and also senses the effect of that motion on the fluid 3. The waves at the top of fluid 3 represent the fluid being a liquid, however whenever the fluid is a gas, those skilled in the art will appreciate that measurand tank 1 can be equipped with a suitable lid and input and output valves. In all cases, one or both surfaces of the piezoelectric resonator need to be in contact with the measurand fluid. Lord Rayleigh, commenting on Stokes' treatment of fluid viscosity, wrote in §347 of his Theory of Sound, Vol. 2, 2nd revised edition, (1896): “The velocity of the fluid in contact with the plane is usually assumed to be the same as that of the plane itself on the apparently sufficient ground that the contrary would imply an infinitely greater smoothness of the fluid with respect to the solid than with respect to itself.” This assumption is implicit throughout this document; it means simply that the fluid immediately adjacent to a moving resonator surface has the same velocity as that surface, and the fluid immediately adjacent to a motionless solid wall has zero velocity. An unbounded Newtonian fluid, i.e., a fluid with shear viscosity, in addition to the usual attributes of mass density, ρ, and elastic stiffnesses, cS and cL, that is in intimate contact with a resonator surface of area A, presents to the surface both shear (S) and longitudinal (L) impedances. These depend on angular frequency, ω=2πf, where f is the frequency in hertz.
Mechanical shear impedance is ZS=A√(jωηρ)=RS+jωLS, where mechanical resistance RS represents shear dissipation and mechanical inductance LS models entrained mass loading. Penetration depth is δ=λ/2π=√(2η/ρω), where λ is the acoustic wavelength. Longitudinal impedance is given by the formula RL (mechanical ohms)=AρvL=A√(ρcL), where vL is the longitudinal of acoustic waves in the fluid. This mechanical resistance represents energy radiating into the measurand fluid; we neglect longitudinal viscosity. These impedances, transformed by a piezoelectric factor, appear in the BVD circuit in series with the R1, L1, and C1 branch. Thus, immittance (a word meaning either impedance or admittance) and/or frequency measurements on a resonator immersed in an unbounded fluid, i.e. when the separation distance (l) from the resonator surface to a confining surface greatly exceeds the penetration depth (δ), yield only the longitudinal elastic stiffness (ρcL) and Newtonian viscosity (ηρ) products.
Although prior art dynamic techniques for measuring fluid shear viscosities using quartz, or other piezoelectrics and the equivalent circuits have proven to be quite beneficial, they are still subject to a number of limitations based on the resonator surface being exposed to a measurand tank where the separation distance (l) between the resonator surface and the confining surfaces of the measurand tank greatly exceeds the penetration depth (δ) of the evanescent shear mode excited by the active element. There is currently no reliable way to measure the quantities η (viscosity) and ρ (mass density) separately. The shortcomings, disadvantages, and limitations of measuring the viscosity-density product in such prior art measurements include, inter alia, the requirement for additional measurements of density. These additional measurements are not a part of an integrated measurement protocol, and are made by other instruments in other setups, leading to inaccuracies due to non-simultaneity of measurements, variations in temperature, and other factors well known to those practiced in the art.
Thus, there has been a long-felt need for a means of obtaining both acoustic shear viscosity and density as separate quantities, simultaneously, and with the same apparatus. The present invention overcomes and obviates the shortcomings, limitations, and disadvantages of prior art measuring systems.